Virginia law requires candidates to submit 10,000 petition signatures, including at least 400 from each congressional district, in order to qualify. Mr. Goode said Tuesday he had submitted about 18,000 as of Aug. 1 and he still has time to collect more before an Aug. 24 deadline.

“I don’t know the details of any investigation,” he said. “I can’t really say, because I don’t know whether it was one petition signature, or 10, or 20, and I don’t know who the person was that was circulating the petition signatures.”

Justin Riemer, deputy secretary for the board, referred questions to Mr. Cuccinelli’s office. A spokeswoman for the attorney general declined to provide additional details, citing the pending investigation.

Mr. Goode, a Democrat-turned-independent-turned Republican, served six terms in Congress representing Virginia’s Southside 5th District before being defeated by Democrat Tom Perriello by 727 votes in 2008.

He’s already made the ballot in more than a dozen other states, but his name recognition and popularity in his former district makes his presence on the ticket especially important in Virginia, a state that could theoretically tip the balance of the presidential election. A recent poll had Mr. Goode taking 9 percent of the vote in the purple state, though early support for third-party candidates typically shrinks dramatically by Election Day.

Between 1996 and 2008 in Virginia, the Constitution Party candidate received an average of about 8,250 votes — figures that would barely register a dent in President Obama’s 2008 victory margin of 234,527 over Sen. John McCain, Arizona Republican.

But Mr. Goode is certainly not a typical Constitution Party candidate, and tightening polls in Virginia indicate that a few thousand votes here or there could end up being the difference.

“You’d have to be on the Mars rover not to know that Republicans don’t want Goode on the ballot,” said Paul Goldman, a longtime Democratic strategist who has advised former Virginia Govs. L. Douglas Wilder and Mark R. Warner, the latter now a U.S. senator. “Does anybody remember Florida? There have been many presidential elections decided by one state.”

Romney supporters have maintained that right-leaning voters want Mr. Obama to lose so badly that they should recognize a vote for a third-party candidate such as Mr. Goode or Libertarian Party candidate Gary E. Johnson effectively amounts to a vote to re-elect the president.

Mr. Goode said Tuesday he doesn’t buy the argument that support for him in Virginia would disproportionately affect Republicans.

“We’re gong to take votes from Romney’s pocket and Obama’s pocket,” he said, citing his support for a moratorium on most green cards allowing for immigrants to work anywhere in the U.S. “I’m sure there are a lot of persons in both parties who agree with me on that issue.”

Virginia’s strict ballot-access rules drew heightened attention during the presidential-primary season, when only Mr. Romney and Rep. Ron Paul of Texas amassed the necessary signatures to qualify for the ballot. In response, Texas Gov. Rick Perry and several other candidates launched an unsuccessful legal challenge to get their names on the ballot.